Plate evaporation under effect of variable intensity energy flows

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Doklady Bashkirskogo Universiteta. 2018. Volume 3. No. 6. pp. 601-607.

Authors

Latypov I. I.*
Bashkir State University, Birsk Branch
49 Internatsionalnaya Street, 452453 Birsk, Republic of Bashkortostan, Russia
Bigaeva L. A.
Bashkir State University, Birsk Branch
49 Internatsionalnaya Street, 452453 Birsk, Republic of Bashkortostan, Russia
Chudinov V. V.
Bashkir State University, Birsk Branch
49 Internatsionalnaya Street, 452453 Birsk, Republic of Bashkortostan, Russia

Abstract

The report poses and solves the problem of finding the temperature distribution in the plate during heating and evaporation under the action of a high-intensity energy flow. The initial boundary value problem is reduced to the solution of a singularly perturbed boundary value problem of the heat equation with nonlinear boundary conditions on moving boundaries. An approximate solution is obtained in the form of an asymptotic expansion of the solution in the Poincaré sense in powers of small parameters, depending on the proximity of the point in question to the boundaries.

Keywords

  • evaporation material
  • heat conduction equation
  • Green’s function
  • boundary value problem
  • asymptotics of the solution
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